# Full refraction in fibre optics

Well in a problem I had to calculate the maximum amount of "reflections" in a glass fibre optic pipe (index of refraction = 1.3, width of 20 micrometer and length of 1 meter). I am a bit blocked on how to calculate this.

I considered first the critical angle $sin(\theta_{cr}) = \frac{1}{n}$ Which came out to be 50 degrees.

I thought: well at critical angle the whole light beam is reflected. $\theta_i = \theta_o = \theta_{cr}$. And the length of each "reflection" would simply be $\frac{d}{\tan(\theta_{cr})}$. Resulting in $\frac{l}{d}$ reflections in the pipe. However this came a bit over 60 000 reflections. While the answer should be around 42 000.

What am I missing here?